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28 July, 06:30

1) Calculate the torque required to accelerate the Earth in 5 days from rest to its present angular speed about its axis. 2) Calculate the energy required. 3) Calculate the average power required.

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  1. 28 July, 06:32
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    a) τ = 4.47746 * 10^25 N-m

    b) E = 2.06301 * 10^13 J

    c) P = 3.25511*10^21 W

    Explanation:

    Given:

    - The radius of earth r = 6.3781*10^6 m

    - The angular speed of earth w = 7.27*10^-5 rad/s

    - The time taken to reach above speed t = 5 yrs = 1.57784760 * 10^8 s

    - The mass of earth m = 5.972 * 10^24 kg

    - The inertia of sphere I = 2/5 * m * r^2

    Solution:

    - The angular acceleration of the earth from rest to w is given by α:

    α = w / t

    α = (7.27*10^-5) / (1.57784760 * 10^8)

    α = 4.60754*10^-13 rad/s^2

    - The required torque τ is given by:

    τ = I*α

    τ = 2/5 * m * r^2 * α

    τ = 2/5 * (5.972 * 10^24) * (6.3781*10^6) ^2 * (4.60754*10^-13)

    τ = 4.47746 * 10^25 N-m

    - The power required P to turn the earth to the speed w is:

    P = τ*w

    P = (4.47746 * 10^25) * (7.27*10^-5)

    P = 3.25511*10^21 W

    - The energy E required is:

    E = P / t

    E = (3.25511*10^21) / (1.57784760 * 10^8)

    E = 2.06301 * 10^13 J
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